Question: Solve for $x$ and $y$ using elimination. ${-x-6y = -11}$ ${-x-5y = -10}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${-x-6y = -11}$ $x+5y = 10$ Add the top and bottom equations together. $-y = -1$ $\dfrac{-y}{{-1}} = \dfrac{-1}{{-1}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {-x-6y = -11}\thinspace$ to find $x$ ${-x - 6}{(1)}{= -11}$ $-x-6 = -11$ $-x-6{+6} = -11{+6}$ $-x = -5$ $\dfrac{-x}{{-1}} = \dfrac{-5}{{-1}}$ ${x = 5}$ You can also plug ${y = 1}$ into $\thinspace {-x-5y = -10}\thinspace$ and get the same answer for $x$ : ${-x - 5}{(1)}{= -10}$ ${x = 5}$